I'm late for something, so will be quick. Looking at it from this perspective, the "nothing" option will decrease any time you increase any density. Thus the expected number of dropped items will increase. There's no way around this.

You won't be able to accomplish your goal if you have spots with guaranteed single items. Once you throw in a loop: "continue until an item is generated" you break things, because you artificially set the likelihood of "nothing".

Okay, yes, this is absolutely true. If we're unwilling to have empty spots in vaults, and unwilling to let unique monsters not drop anything, then we're back in the position of "the frequency of one item affects the frequency of all other items." Thanks for the clarification. Hence why my suggestion was that for situations where currently we say "we guarantee an item here", we should instead say "we will make N attempts to generate an item." Failure is still an option, but its likelihood is reduced by the repeats, without the relative frequencies of the item pool changing in any way.

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None of this matters, of course. Any method is fine, so long as you carefully rebalance after each change. The real problem is that so many of you want to make the sexy flashy change, but are unwilling to do the important gruntwork of rebalancing. That isn't about statistics. It's about getting experts to play and then listening to them. Reverting a bad change shouldn't be anathema, and easily 50% of changes are bad changes. Personally I believe Sturgeon's law applies here, as it does so often everywhere.

Absolutely true! These things do need to just be iterated on over and over again until the balance is right. My goal with this proposal was to make it easier to do this. Right now balancing item frequencies is (to make a rather outdated reference) like trying to eliminate a bubble in some wallpaper -- if you press it down in one place, it'll pop up again in another place. The interconnectedness of all things makes it impossible to make a small isolated change. Whereas with my proposal, we absolutely can say e.g. "Amulets of Trickery are too common", make them less common, and not worry that now Amulets of Weaponmastery are now too common.

My hope is that if we make the job easier, then more people will be willing to tackle it.

Eddie--
You are both saying the same thing: to reduce junk, you must reduce drops, not increase good items. I'd do it by just resurrecting the original model, and simply removing a fraction of the junk from the drops--which is what Derakon is suggesting as well.

You may be right. I do feel like my proposed method would be more elegant implementation-wise and easier to make balance changes to, though. I believe fizzix has more experience on this side of things, though, so I'd also love to hear his opinion.

I do see the appeal of your approach, and I guess in fact it could be implemented at a stroke just by summing over all the base item probabilities for each level, and then setting your "1 million" figure as the maximum of those (or maybe something a little bigger). I will think some more.

Not wanting to speak for fizzix, but he was one of the chief proponents of collecting game stats, which essentially try to solve this via posterior rather than prior probabilities - you just generate 100 levels (lots of times), bin up all the items, and see what you got. Then adjust things that look wrong.

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I do see the appeal of your approach, and I guess in fact it could be implemented at a stroke just by summing over all the base item probabilities for each level, and then setting your "1 million" figure as the maximum of those (or maybe something a little bigger). I will think some more.

Not wanting to speak for fizzix, but he was one of the chief proponents of collecting game stats, which essentially try to solve this via posterior rather than prior probabilities - you just generate 100 levels (lots of times), bin up all the items, and see what you got. Then adjust things that look wrong.

I think the two approaches may actually be complementary? Derakon's idea will make the "adjust" bit of fizzix's approach a lot easier, AFAICT.

I think the two approaches may actually be complementary? Derakon's idea will make the "adjust" bit of fizzix's approach a lot easier, AFAICT.

Indeed. My proposal makes it straightforward to know the percentage of "item attempts" that will be a specific item at a given depth, but it doesn't make any statements about how many actual items that is in practice, since that depends on floor item density, number of monsters, number of vaults, etc. The stats are absolutely still necessary for making informed decisions.